Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
538 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21424164 | C2 | semidirect |
| 3. #21421921 | C2 | semidirect |
| 4. #21421916 | C2 | semidirect |
| 5. C4×C22⋊C8×C59 | C2 | semidirect |
| 186. C4×C22⋊C8 | D59 | semidirect |
| 215. C59 | #7670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432397 | 2 |
| #21424164 | 2 |
| #21421921 | 2 |
| #21421916 | 2 |
| C4×C22⋊C8×C59 | 2 |
| #7670 | 59 |